The present invention relates to a new and distinct variety of yellow peach tree, Prunus persica (L.) Batsch, which has been given the variety denomination ‘CRISPLATE’. This new tree produces fruits with a long shelf life without alteration both on the tree after growth completion and after harvesting, very good eating quality, clingstone yellow flesh fruits for fresh market in September in the Pyrénées-Orientales department (an administrative district), France. Contrast is made to its female parent ‘JULIENICE’ (U.S. Plant Pat. No. 20,472) yellow peach tree and to its male parent ‘NECTALADY’ (U.S. Plant Pat. No. 17,580) yellow nectarine tree, for reliable description. ‘CRISPLATE’ is a promising candidate for commercial success in that it has very attractive fruits with very long shelf life without alteration both before and after harvesting.